Help Please

Any help on this problem would be greatly appreciated. It deals with multiple integration:

Find the centre of mass (x,y) of the lamina which occupies the region:
36 less than or equal to (x^2) + (y^2) less than or equal to 49
y greater or equal to 0
if the density at any point is proportional to the distance from the origin.

Any help on this problem would be greatly appreciated. It deals with multiple integration:

Find the centre of mass (x,y) of the lamina which occupies the region:
36 less than or equal to (x^2) + (y^2) less than or equal to 49
y greater or equal to 0
if the density at any point is proportional to the distance from the origin.

Thanks in advance.

Mike

Below is the diamgram of the region.
In order to solve this problem you need to find the countinous density function. Which you say is proportional to the distance. I take this to mean that you are saying directly proportional right? Then you have, for some constant of proportionality.
In mathematical terms,
Thus,

In order to find the center of mass you first need to find the mass. Which in this case is,
Thus,
I believe it is easier by converting to polar cordinates.
Thus,
Thus,--->Mass
----------
I will continue later.

Any help on this problem would be greatly appreciated. It deals with multiple integration:

Find the centre of mass (x,y) of the lamina which occupies the region:
36 less than or equal to (x^2) + (y^2) less than or equal to 49
y greater or equal to 0
if the density at any point is proportional to the distance from the origin.

Thanks in advance.

Mike

I will rewrite the definition of the region more clearly for you:

,

which is the top half of the shaded region in hacker's diagram.

RonL

(If the region had corresponded to hackers shaded region the centre
of mass would of course have been at by symmetry)

Any help on this problem would be greatly appreciated. It deals with multiple integration:

Find the centre of mass (x,y) of the lamina which occupies the region:
36 less than or equal to (x^2) + (y^2) less than or equal to 49
y greater or equal to 0
if the density at any point is proportional to the distance from the origin.